Some very good answers have been posted. As for Rumba, in some cases (more common in newer Rumba music) the rhythm is naturally SQQ, while in other cases it is QQS. As for the dance figures, you were probably taught them using one of the two conventions. I was taught by instructors who followed the QQS convention. I have a syllabus I purchased used from an instructor that (the syllabus) uses the SQQ convention. The instructor marked it up so that he could teach the patterns with the QQS rhythm. It's just a matter of where you start. If you listen to the music you can hear the S and you can hear the QQ. Jump in on whichever beat coincides with how you learned the figures. Once you are dancing it doesn't matter.

As for Cha-Cha, one instructor I know is very insistent (almost pedantic) in insisting that "it's Cha-Cha, NOT Cha-Cha_Cha." She breaks down the figures using the 1-2-3-4& rhythm. That is, she matches one measure of dance steps to one measure of music. If (for example) you are dancing the basic movement, it's customary to start with a side step on the 1 beat. In her approach, that's step 1. Her step 1 is on beat 1 of the music. Next comes a rock step (2-3) followed by a chasse (or side-close; I may be using the term "chasse" incorrectly) on the 4&. That finishes the measure. The next step, a side step, starts the next measure, and it also starts the rhythm again. Simple and logical, and it fits the music. In the other (Cha-Cha-Cha) approach the first side step (1) is a "prep step." Then you dance 2-3-4&-1 (or 2, 3, cha-cha-cha). That means that the basic rhythm straddles two measures: it starts on beat 2 (the up beat) and the final step is on the first beat of the next measure. A little more complicated to analyze.

It comes down to the difference between rhythm and timing. Rhythm is the pattern of slows and quicks (or quicks and ands), while timing refers to which beat you start the rhythm with. In one case (one version of the rhythm) you start (timing) on beat 1. In the other case (the other version of the rhythm) you start (timing) on beat 2. Once again, it doesn't really matter once you are dancing. Do whatever works for you.